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In how many ways can 3 portraits be mounted on 3 of the four walls ins 17 Feb 2017, 01:57
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E
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61% (01:02) correct 39% (01:07) wrong based on 238 sessions

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In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Source: https://www.GMATinsight.com

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In how many ways can 3 portraits be mounted on 3 of the four walls ins 17 Feb 2017, 02:40
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In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Source: https://www.GMATinsight.com

Hi,

First, select 3 walls out of the 4 given walls = \(^4C_{3}\) = 4 ways

AND

Three different portraits can be arranged in 3! ways = 6 ways.

Total number of ways = 4 * 6 = 24 ways.

Thanks.
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In how many ways can 3 portraits be mounted on 3 of the four walls ins 17 Feb 2017, 03:03
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P1 has 4 options
P2 has 3 options
P3 has 2 options

So 4*3*2
24 option e

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In how many ways can 3 portraits be mounted on 3 of the four walls ins 03 Mar 2017, 08:54
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This is my approach:

As there are 3 walls there can be 3 places for portraits on each. So (3+3+3=9) 9C3=24

Hope this will help
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In how many ways can 3 portraits be mounted on 3 of the four walls ins 27 May 2019, 05:34
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In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Source: https://www.GMATinsight.com

The number of ways to pick 3 walls from 4 is 4C3 = 4. Once 3 walls are picked, the number of ways to mount the portraits onto the walls is 3! = 6. Therefore, there are a total of 4 x 6 = 24 ways to mount 3 portraits on 3 of the four walls inside a room.

Answer: E
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In how many ways can 3 portraits be mounted on 3 of the four walls ins 01 Feb 2021, 12:18
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In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Source: https://www.GMATinsight.com

The number of ways to pick 3 walls from 4 is 4C3 = 4. Once 3 walls are picked, the number of ways to mount the portraits onto the walls is 3! = 6. Therefore, there are a total of 4 x 6 = 24 ways to mount 3 portraits on 3 of the four walls inside a room.

Answer: E

Hi can someone help on this one? Why is it that 3 different portraits can be mounted on 3 walls 3! ways?
How come it's not 6! / 3! x 3! = 20 ways?

ppp ||| <---- 3 portraits and 3 divisors so 6!/3! x 3!

I guess the idea here is that there can be a maximum of one portrait per wall...
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In how many ways can 3 portraits be mounted on 3 of the four walls ins 03 Mar 2021, 11:52
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In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Source: https://www.GMATinsight.com

The number of ways to pick 3 walls from 4 is 4C3 = 4. Once 3 walls are picked, the number of ways to mount the portraits onto the walls is 3! = 6. Therefore, there are a total of 4 x 6 = 24 ways to mount 3 portraits on 3 of the four walls inside a room.

Answer: E

Hi can someone help on this one? Why is it that 3 different portraits can be mounted on 3 walls 3! ways?
How come it's not 6! / 3! x 3! = 20 ways?

ppp ||| <---- 3 portraits and 3 divisors so 6!/3! x 3!

I guess the idea here is that there can be a maximum of one portrait per wall...

Response:

As a matter of fact, you are correct; the question should have said “one painting per wall.” However, your answer of 20 is not the correct answer for that scenario (unless the paintings are identical, which we know is not the case). If we can mount more than one painting per wall, the number of ways should increase. If that was the case, you would solve “prq |||” instead of “ppp |||”.
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In how many ways can 3 portraits be mounted on 3 of the four walls ins 12 Feb 2024, 06:48
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Hi everyone,

In case more than one painting could have been hung on each wall, what would the solution have been?
Four alternatives for each painting, right?
So 4^3, correct?

And what about if also the order (let's say from left to right, or from bottom to top) of two or more paintings on the same wall would have mattered?
4 * 5 * 6 = 120
Is it correct?

Thanks

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